Suddenly I have a very brief right click menu that does not offer the option of creating shortcut. I can only save a webpage as a downloaded file rather than creating a desktop shortcut to it. Very annoying.

I'm not sure how it changed without you changing the configuration, but I can tell you that it's fairly easy to change back:
Go to - Start -> Control panel -> Mouse -> Uncheck the box next to "Switch primary and secondary buttons" -> Click on OK and you're good to go.